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eigen/test/array_cwise.cpp
Antonio Sanchez c65c2b31d4 Make half/bfloat16 constructor take inputs by value, fix powerpc test. 
Since `numeric_limits<half>::max_exponent` is a static inline constant,
it cannot be directly passed by reference. This triggers a linker error
in recent versions of `g++-powerpc64le`.

Changing `half` to take inputs by value fixes this.  Wrapping
`max_exponent` with `int(...)` to make an addressable integer also fixes this
and may help with other custom `Scalar` types down-the-road.

Also eliminated some compile warnings for powerpc.
2021-02-27 21:32:06 +00:00

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
// Test the corner cases of pow(x, y) for real types.
template<typename Scalar>
void pow_test() {
const Scalar zero = Scalar(0);
const Scalar eps = std::numeric_limits<Scalar>::epsilon();
const Scalar one = Scalar(1);
const Scalar two = Scalar(2);
const Scalar three = Scalar(3);
const Scalar sqrt_half = Scalar(std::sqrt(0.5));
const Scalar sqrt2 = Scalar(std::sqrt(2));
const Scalar inf = std::numeric_limits<Scalar>::infinity();
const Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
const Scalar min = (std::numeric_limits<Scalar>::min)();
const Scalar max = (std::numeric_limits<Scalar>::max)();
const Scalar max_exp = (static_cast<Scalar>(int(std::numeric_limits<Scalar>::max_exponent)) * Scalar(EIGEN_LN2)) / eps;
const static Scalar abs_vals[] = {zero,
denorm_min,
min,
eps,
sqrt_half,
one,
sqrt2,
two,
three,
max_exp,
max,
inf,
nan};
const int abs_cases = 13;
const int num_cases = 2*abs_cases * 2*abs_cases;
// Repeat the same value to make sure we hit the vectorized path.
const int num_repeats = 32;
Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
int count = 0;
for (int i = 0; i < abs_cases; ++i) {
const Scalar abs_x = abs_vals[i];
for (int sign_x = 0; sign_x < 2; ++sign_x) {
Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
for (int j = 0; j < abs_cases; ++j) {
const Scalar abs_y = abs_vals[j];
for (int sign_y = 0; sign_y < 2; ++sign_y) {
Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
for (int repeat = 0; repeat < num_repeats; ++repeat) {
x(repeat, count) = x_case;
y(repeat, count) = y_case;
}
++count;
}
}
}
}
Array<Scalar, Dynamic, Dynamic> actual = x.pow(y);
const Scalar tol = test_precision<Scalar>();
bool all_pass = true;
for (int i = 0; i < 1; ++i) {
for (int j = 0; j < num_cases; ++j) {
Scalar e = static_cast<Scalar>(std::pow(x(i,j), y(i,j)));
Scalar a = actual(i, j);
bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e));
all_pass &= !fail;
if (fail) {
std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl;
}
}
}
VERIFY(all_pass);
}
template<typename ArrayType> void array(const ArrayType& m)
{
typedef typename ArrayType::Scalar Scalar;
typedef typename ArrayType::RealScalar RealScalar;
typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols);
ArrayType m4 = m1; // copy constructor
VERIFY_IS_APPROX(m1, m4);
ColVectorType cv1 = ColVectorType::Random(rows);
RowVectorType rv1 = RowVectorType::Random(cols);
Scalar s1 = internal::random<Scalar>(),
s2 = internal::random<Scalar>();
// scalar addition
VERIFY_IS_APPROX(m1 + s1, s1 + m1);
VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
m3 = m1;
m3 += s2;
VERIFY_IS_APPROX(m3, m1 + s2);
m3 = m1;
m3 -= s1;
VERIFY_IS_APPROX(m3, m1 - s1);
// scalar operators via Maps
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 - m2);
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 + m2);
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 * m2);
m3 = m1;
m2 = ArrayType::Random(rows,cols);
m2 = (m2==0).select(1,m2);
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 / m2);
// reductions
VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
using std::abs;
VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
// vector-wise ops
m3 = m1;
VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
m3 = m1;
VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
m3 = m1;
VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
m3 = m1;
VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
// Conversion from scalar
VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
typedef Array<Scalar,
ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
ArrayType::Options> FixedArrayType;
{
FixedArrayType f1(s1);
VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
FixedArrayType f2(numext::real(s1));
VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
FixedArrayType f3((int)100*numext::real(s1));
VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
f1.setRandom();
FixedArrayType f4(f1.data());
VERIFY_IS_APPROX(f4, f1);
}
#if EIGEN_HAS_CXX11
{
FixedArrayType f1{s1};
VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
FixedArrayType f2{numext::real(s1)};
VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
FixedArrayType f3{(int)100*numext::real(s1)};
VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
f1.setRandom();
FixedArrayType f4{f1.data()};
VERIFY_IS_APPROX(f4, f1);
}
#endif
// pow
VERIFY_IS_APPROX(m1.pow(2), m1.square());
VERIFY_IS_APPROX(pow(m1,2), m1.square());
VERIFY_IS_APPROX(m1.pow(3), m1.cube());
VERIFY_IS_APPROX(pow(m1,3), m1.cube());
VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
// Check possible conflicts with 1D ctor
typedef Array<Scalar, Dynamic, 1> OneDArrayType;
{
OneDArrayType o1(rows);
VERIFY(o1.size()==rows);
OneDArrayType o2(static_cast<int>(rows));
VERIFY(o2.size()==rows);
}
#if EIGEN_HAS_CXX11
{
OneDArrayType o1{rows};
VERIFY(o1.size()==rows);
OneDArrayType o4{int(rows)};
VERIFY(o4.size()==rows);
}
#endif
// Check possible conflicts with 2D ctor
typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
typedef Array<Scalar, 2, 1> ArrayType2;
{
TwoDArrayType o1(rows,cols);
VERIFY(o1.rows()==rows);
VERIFY(o1.cols()==cols);
TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols));
VERIFY(o2.rows()==rows);
VERIFY(o2.cols()==cols);
ArrayType2 o3(rows,cols);
VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols));
VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
}
#if EIGEN_HAS_CXX11
{
TwoDArrayType o1{rows,cols};
VERIFY(o1.rows()==rows);
VERIFY(o1.cols()==cols);
TwoDArrayType o2{int(rows),int(cols)};
VERIFY(o2.rows()==rows);
VERIFY(o2.cols()==cols);
ArrayType2 o3{rows,cols};
VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
ArrayType2 o4{int(rows),int(cols)};
VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
}
#endif
}
template<typename ArrayType> void comparisons(const ArrayType& m)
{
using std::abs;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols),
m4 = m1;
m4 = (m4.abs()==Scalar(0)).select(1,m4);
VERIFY(((m1 + Scalar(1)) > m1).all());
VERIFY(((m1 - Scalar(1)) < m1).all());
if (rows*cols>1)
{
m3 = m1;
m3(r,c) += 1;
VERIFY(! (m1 < m3).all() );
VERIFY(! (m1 > m3).all() );
}
VERIFY(!(m1 > m2 && m1 < m2).any());
VERIFY((m1 <= m2 || m1 >= m2).all());
// comparisons array to scalar
VERIFY( (m1 != (m1(r,c)+1) ).any() );
VERIFY( (m1 > (m1(r,c)-1) ).any() );
VERIFY( (m1 < (m1(r,c)+1) ).any() );
VERIFY( (m1 == m1(r,c) ).any() );
// comparisons scalar to array
VERIFY( ( (m1(r,c)+1) != m1).any() );
VERIFY( ( (m1(r,c)-1) < m1).any() );
VERIFY( ( (m1(r,c)+1) > m1).any() );
VERIFY( ( m1(r,c) == m1).any() );
// test Select
VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
for (int j=0; j<cols; ++j)
for (int i=0; i<rows; ++i)
m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
.select(ArrayType::Zero(rows,cols),m1), m3);
// shorter versions:
VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
.select(0,m1), m3);
VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
.select(m1,0), m3);
// even shorter version:
VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
// count
VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
// and/or
VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
RealScalar a = m1.abs().mean();
VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
typedef Array<Index, Dynamic, 1> ArrayOfIndices;
// TODO allows colwise/rowwise for array
VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
}
template<typename ArrayType> void array_real(const ArrayType& m)
{
using std::abs;
using std::sqrt;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols),
m4 = m1;
m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4);
Scalar s1 = internal::random<Scalar>();
// these tests are mostly to check possible compilation issues with free-functions.
VERIFY_IS_APPROX(m1.sin(), sin(m1));
VERIFY_IS_APPROX(m1.cos(), cos(m1));
VERIFY_IS_APPROX(m1.tan(), tan(m1));
VERIFY_IS_APPROX(m1.asin(), asin(m1));
VERIFY_IS_APPROX(m1.acos(), acos(m1));
VERIFY_IS_APPROX(m1.atan(), atan(m1));
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
#if EIGEN_HAS_CXX11_MATH
VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1)));
VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1)));
VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1)));
#endif
VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
VERIFY_IS_APPROX(m1.arg(), arg(m1));
VERIFY_IS_APPROX(m1.round(), round(m1));
VERIFY_IS_APPROX(m1.rint(), rint(m1));
VERIFY_IS_APPROX(m1.floor(), floor(m1));
VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
VERIFY_IS_APPROX(m1.abs(), abs(m1));
VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
VERIFY_IS_APPROX(m1.square(), square(m1));
VERIFY_IS_APPROX(m1.cube(), cube(m1));
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(m1.sign(), sign(m1));
VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all());
// avoid inf and NaNs so verification doesn't fail
m3 = m4.abs();
VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3)));
VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3)));
VERIFY_IS_APPROX(m3.log(), log(m3));
VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
VERIFY_IS_APPROX(m3.log10(), log10(m3));
VERIFY_IS_APPROX(m3.log2(), log2(m3));
VERIFY((!(m1>m2) == (m1<=m2)).all());
VERIFY_IS_APPROX(sin(m1.asin()), m1);
VERIFY_IS_APPROX(cos(m1.acos()), m1);
VERIFY_IS_APPROX(tan(m1.atan()), m1);
VERIFY_IS_APPROX(sinh(m1), Scalar(0.5)*(exp(m1)-exp(-m1)));
VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1)));
VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1))));
VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1))));
VERIFY_IS_APPROX(arg(m1), ((m1<Scalar(0)).template cast<Scalar>())*Scalar(std::acos(Scalar(-1))));
VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all());
VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all());
VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all());
VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all());
VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all());
VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all());
VERIFY((Eigen::isinf)(m4/Scalar(0)).all());
VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all());
VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
VERIFY_IS_APPROX(m3, sqrt(abs2(m3)));
VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1));
VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1));
if(!NumTraits<Scalar>::IsComplex)
VERIFY_IS_APPROX(numext::real(m1), m1);
// shift argument of logarithm so that it is not zero
Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m3) + smallNumber));
VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + smallNumber));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber));
VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
// Avoid inf and NaN.
m3 = (m1.square()<NumTraits<Scalar>::epsilon()).select(Scalar(1),m3);
VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
pow_test<Scalar>();
VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10)));
VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2)));
// scalar by array division
const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
// check inplace transpose
m3 = m1;
m3.transposeInPlace();
VERIFY_IS_APPROX(m3, m1.transpose());
m3.transposeInPlace();
VERIFY_IS_APPROX(m3, m1);
}
template<typename ArrayType> void array_complex(const ArrayType& m)
{
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2(rows, cols),
m4 = m1;
m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
Array<RealScalar, -1, -1> m3(rows, cols);
for (Index i = 0; i < m.rows(); ++i)
for (Index j = 0; j < m.cols(); ++j)
m2(i,j) = sqrt(m1(i,j));
// these tests are mostly to check possible compilation issues with free-functions.
VERIFY_IS_APPROX(m1.sin(), sin(m1));
VERIFY_IS_APPROX(m1.cos(), cos(m1));
VERIFY_IS_APPROX(m1.tan(), tan(m1));
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
VERIFY_IS_APPROX(m1.arg(), arg(m1));
VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
VERIFY_IS_APPROX(m1.log(), log(m1));
VERIFY_IS_APPROX(m1.log10(), log10(m1));
VERIFY_IS_APPROX(m1.log2(), log2(m1));
VERIFY_IS_APPROX(m1.abs(), abs(m1));
VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
VERIFY_IS_APPROX(m1.square(), square(m1));
VERIFY_IS_APPROX(m1.cube(), cube(m1));
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(m1.sign(), sign(m1));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.);
// Check for larger magnitude complex numbers that expm1 matches exp - 1.
VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.);
VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
VERIFY_IS_APPROX(logistic(m1), (1.0/(1.0 + exp(-m1))));
for (Index i = 0; i < m.rows(); ++i)
for (Index j = 0; j < m.cols(); ++j)
m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real());
VERIFY_IS_APPROX(arg(m1), m3);
std::complex<RealScalar> zero(0.0,0.0);
VERIFY((Eigen::isnan)(m1*zero/zero).all());
#if EIGEN_COMP_MSVC
// msvc complex division is not robust
VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
#else
#if EIGEN_COMP_CLANG
// clang's complex division is notoriously broken too
if((numext::isinf)(m4(0,0)/RealScalar(0))) {
#endif
VERIFY((Eigen::isinf)(m4/zero).all());
#if EIGEN_COMP_CLANG
}
else
{
VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
}
#endif
#endif // MSVC
VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag())));
VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
VERIFY_IS_APPROX(log2(m1), log(m1)/log(2));
VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
// scalar by array division
Scalar s1 = internal::random<Scalar>();
const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
// check inplace transpose
m2 = m1;
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1.transpose());
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1);
// Check vectorized inplace transpose.
ArrayType m5 = ArrayType::Random(131, 131);
ArrayType m6 = m5;
m6.transposeInPlace();
VERIFY_IS_APPROX(m6, m5.transpose());
}
template<typename ArrayType> void min_max(const ArrayType& m)
{
typedef typename ArrayType::Scalar Scalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols);
// min/max with array
Scalar maxM1 = m1.maxCoeff();
Scalar minM1 = m1.minCoeff();
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
// min/max with scalar input
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
VERIFY_IS_APPROX(m1, (m1.max)( minM1));
// min/max with various NaN propagation options.
if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) {
m1(0,0) = std::numeric_limits<Scalar>::quiet_NaN();
maxM1 = m1.template maxCoeff<PropagateNaN>();
minM1 = m1.template minCoeff<PropagateNaN>();
VERIFY((numext::isnan)(maxM1));
VERIFY((numext::isnan)(minM1));
maxM1 = m1.template maxCoeff<PropagateNumbers>();
minM1 = m1.template minCoeff<PropagateNumbers>();
VERIFY(!(numext::isnan)(maxM1));
VERIFY(!(numext::isnan)(minM1));
}
}
EIGEN_DECLARE_TEST(array_cwise)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
CALL_SUBTEST_2( array(Array22f()) );
CALL_SUBTEST_3( array(Array44d()) );
CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( array(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
CALL_SUBTEST_2( comparisons(Array22f()) );
CALL_SUBTEST_3( comparisons(Array44d()) );
CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
CALL_SUBTEST_2( min_max(Array22f()) );
CALL_SUBTEST_3( min_max(Array44d()) );
CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
CALL_SUBTEST_2( array_real(Array22f()) );
CALL_SUBTEST_3( array_real(Array44d()) );
CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_7( array_real(Array<Eigen::half, 32, 32>()) );
CALL_SUBTEST_8( array_real(Array<Eigen::bfloat16, 32, 32>()) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
ArrayBase<Xpr>
>::value));
}
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